The Big Question

What is in the world?

The World of Things

One of the points of chapter 9 is to argue that the world doesn’t consist of just things.

Things aren’t enough to explain all the facts.

Two Attempts

There are others too, but we’ll focus on two

1. Objects and resemblances (which we project)
2. Sets of objects

Resemblance

There are just things like Squid, and Tree, and you and me. There is no SLEEPING or LOVES.

It’s just that we humans, perhaps for good practical reasons, project patterns we see onto the world.

Russell’s Objection to This

What does it mean to say that something else resembles the paradigm of a sleeping thing.

That looks like a universal too.

To say that to be sleeping just is to resemble our paradigm of a sleeper is not to remove universals; it’s to replace a universal property (like SLEEPING) with a universal relation (like RESEMBLES)

Sets

A more modern approach is to say that there are just objects, and sets of objects.

More or less equivalently, we can say that there are objects, and two truth values (T and F), and functions from things we recognise into things we recognise.

So a predicate, like ‘is sleeping’ or ‘is cute’ is a function from things to truth values; intuitively, the things that have the property are mapped to T and everything else to F.

Semantics

This is actually the start of a rather nice theory of word meanings, and one you might study a bit more in other philosophy or linguistics classes.

One advantage is that it generalises nicely. Think about the (true) sentence Squid is very cute.

Russell would say that ‘Squid’ picks out Squid, and ‘cute’ picks out CUTENESS, but what does ‘very’ pick out? Is there a universal of VERYNESS?

Semantics

Here’s a nice theory. ‘Very’ is a function from predicate meanings to predicate meanings. (Where a predicate meaning is a function from objects to truth values) In a sentence it says “Give me a predicate, and I’ll give you a new predicate”.

What’s the structure of that function? Well, it returns a new predicate that only says T to things that are really solid cases of T in the original.

This isn’t a semantics class, but this idea of treating all words (except names) as functions of more or less complexity is rather elegant.

Metaphysics

But we’re going to focus on metaphysics, not semantics.

Instead of the universals that Russell posits, could we just have sets?

Relations

Russell’s big concern is that a lot of other theories don’t have place for relations.

But the sets theory does.

A relation is just a set of ordered pairs.

And an ordered pair is just, well it’s something a bit like a set.

Problems

1. Sets are spooky.
2. There are too many sets.

Spooky

The people who think that we should do away with universals and just have sets typically think that there is something mysterious, spooky, about these Platonic universals.

But sets are just as weird, as becomes clear as soon as you think about singletons, i.e., sets with just one member.

Squid’s singleton is not identical to Squid, but it isn’t anywhere other than where Squid is. It seems a really odd thing to have to posit, just as mysterious as a universal like SLEEPING.

Too Many

But the big problem is that there are too many sets.

• There is a set of all the things that are sleeping.
• But there is also a set of all the things that are sleeping plus this remote control.
• And there is a set of all the things that are sleeping except Squid.
• These cause all sorts of problems.

Problems from Abundance

The vast number of sets causes all sorts of challenges.

• How do we learn ‘sleeeping’ means this particular set not some nearby one?
• That Squid is sleeping explains some things. That Squid is in a set doesn’t explain anything, because set-membership is cheap.
• That Squid is sleeping implies she resembles, in some respect, other sleeping things. But common set-membership does not imply resemblance, since any two things no matter how disjoint are in a set together.

Abundant or Sparse

• Russell seems to think that there are lots of universals; maybe one for each word.
• That’s not a common view these days.
• It’s more common to say that there are a handful of universals.
• In particular, there are only as many universals as are needed to explain facts of resemblance.

Abundant or Sparse

Indeed, for some contemporary(ish) defenders of universals, explaining resemblance is the job that universals do.

The Australian philosopher David Armstrong, who for a while was the most prominent defender of (something like) the theory of universals Russell endorses, thought there were exactly as many universals as were needed to explain resemblance between objects.

Abundant or Sparse

But you don’t need universals for every predicate to do that. You certainly don’t need them for compound predicates.

So, it being fall, think about the predicate in This is a pumpkin spice latte.

It’s (somewhat) plausible that PUMPKIN, SPICE, and LATTE are all universals.

But we don’t need another universal PUMPKIN SPICE LATTE to explain what all pumpkin spice lattes have in common. We can do that by explaining that they are all lattes, and that they are all pumpkin spiced.

Very Tricky Question

The pumpkin spice latte raises a problem that I’m just going to mention, and then leave for metaphysics classes.

In that phrase, ‘pumpkin’ does not immediately modify ‘latte’, it modifies ‘spice’. It tells you what kind of spice is in the drink.

You might ask, as a sort of metaphysical parallel to that, whether universals themselves can have properties.

Very Tricky Question

On the one hand yes sure of course they do: HONESTY is a virtue, for example.

On the other hand, the logical and metaphysical troubles that arise when you allow this are immense, and it’s really hard to not contradict yourself if you go this way.

(The problems start with things like the property of being a property that doesn’t apply to itself. That’s very much not our problem today.)

What’s called higher-order metaphysics is about this, among other questions.

Universals Everywhere

Russell says that every sentence has a universal in it.

• Here’s a tricky case for that: Peter Parker is Spiderman.
• If you don’t like fictional examples, use Onika Tanya Maraj-Petty is Nicki Minaj.
• That’s true, and it does have a verb in it.
• Is that a universal? I think Russell would say yes.
• But the ‘is’ there is identity, and being self-identical is not a way in which Spiderman resembles anything, since everything is self-identical.

Immanent or Platonic

Russell says that universals have being but not existence, because they aren’t in the world.

There’s a rival view (held by Armstrong, following Aristotle) that universals are indeed in the world, and they are (in some sense) in the things that instantiate them.

So HUMANITY isn’t something that has being in Platonic heaven, it’s in this room (and many other rooms).

I’m mostly just flagging this as an interesting (and long-running) debate that arises around here.

Mind-Dependent

Russell is very concerned to argue that universals represent mind-independent facts about reality.

But the example he uses for this is completely wild, and doesn’t really make the point.

Edinburgh is north of London.

Mind-Dependent

I think cities, like Edinburgh and London, are mind-dependent entities.

• I don’t just mean that they were caused to come into being by minds, though that’s true.
• Nor do I just mean that the fact that “London” means London is something that is mind-dependent, though that’s true too.
• I mean what London itself is is mind-dependent, and the same goes for all other cities.

Ann Arbor

Where is Ann Arbor? The boundaries are of course written down in a rulebook somewhere, but what makes them the boundaries.

I think it’s the fact that we all agree that those regulations are the ones that matter. And agreeing is a thing that minds do.

Ann Arbor

If we all came to believe that UM was in a separate city from Ann Arbor, perhaps a new city called Wolverineville, that would kind of do it; Ann Arbor would no longer contain UM.

• The metaphysics of cities I think is really hard, and the toy theory Russell has, that ‘London’ names a point on the earth’s surface, isn’t actually that plausible.
• It’s conceptually possible that London is 10 miles west of where it used to be, but it’s not conceptually possible that a point is ten miles west of where it used to be.

Russell’s Other Example

The other example Russell uses is WHITENESS, but I think that’s really mind-dependent.

Whether something is white just is whether it looks white to normal observers in normal conditions. That’s mind-dependence.

Mind-Independence

I’m mostly kvetching here about examples.

I think Russell is probably right.

That there are various universals concerning nuclear fusion, and that some of those are instantiated by things going on inside the sun seems both true and mind-independent.

But it’s kind of bizarre to me which examples he picked.

Truth

What is truth? Read chapter 12 to maybe find out.